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pottersheep

Grade 12 math help please!! For what value of b will the polynomial p(x) = -2x^3 + bx^2 - 5x +2 have the same remainder when it is divided by x - 2 and x+1?

  • one year ago
  • one year ago

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  1. TAKEBACKMATH
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    okay I will show you:

    • one year ago
  2. pottersheep
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    thank you so much!

    • one year ago
  3. pottersheep
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    :(

    • one year ago
  4. TAKEBACKMATH
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    thinking

    • one year ago
  5. pottersheep
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    oh ok sorry

    • one year ago
  6. TAKEBACKMATH
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    sorry, it too late for me I will hand this over to lonesome else?

    • one year ago
  7. pottersheep
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    ok

    • one year ago
  8. pottersheep
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    thanks anyways

    • one year ago
  9. Callisto
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    Here it goes~ Have you learnt remainder theorem yet?

    • one year ago
  10. Callisto
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    @pottersheep Are you there??

    • one year ago
  11. pottersheep
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    Yes sorry, we have!

    • one year ago
  12. Callisto
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    So, let R be the remainder when p(x) is divided by x-2. By remainder theorem, what would you get? I mean p(_) = ...?

    • one year ago
  13. pottersheep
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    ok one sec

    • one year ago
  14. pottersheep
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    So i'd sub in 2 for x

    • one year ago
  15. Callisto
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    Yup!

    • one year ago
  16. pottersheep
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    3?

    • one year ago
  17. pottersheep
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    sorryryyryryryr

    • one year ago
  18. pottersheep
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    Sorry what do I do with the b though?

    • one year ago
  19. pottersheep
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    4b -24

    • one year ago
  20. Callisto
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    Right, so for p(2), you get p(2) = 4b - 24 = R, agree? (By remainder theorem, p(a) = R , when p(x) is divided by x-a)

    • one year ago
  21. pottersheep
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    Right, okay

    • one year ago
  22. Callisto
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    And what is the remainder when p(x) is divided by x+1 ?

    • one year ago
  23. pottersheep
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    b - 5

    • one year ago
  24. Callisto
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    Not really.. Remainder = p(-1) = -2(-1)^3 + b(-1)^2 - 5(-1) +2 = ...?

    • one year ago
  25. pottersheep
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    Opps, sorry! I subbed in 1!

    • one year ago
  26. pottersheep
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    9??

    • one year ago
  27. pottersheep
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    b + 9!

    • one year ago
  28. Callisto
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    Yes. Note that the remainder is p(x) = R when p(x) is divided by x-a. Now, p(x) is divided by x+1, so a = -1 in the case. [ x-(-1) = x+1]

    • one year ago
  29. pottersheep
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    True, sorry!

    • one year ago
  30. Callisto
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    From the question, the polynomial p(x) = -2x^3 + bx^2 - 5x +2 have the same remainder when it is divided by x - 2 and x+1. So, equate the two remainder you got and solve b. Got it?

    • one year ago
  31. Callisto
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    Oh.. It's okay!

    • one year ago
  32. pottersheep
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    Ohhhhhhhhh, so make them equal to each other?? Yes I get it, thank you!!!!!!

    • one year ago
  33. Callisto
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    Yes. Since they have the SAME remainder! You're welcome :)

    • one year ago
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